Is Color Management applied to ColorRamps?
To answer the subject line, no.

But wait, there's more!

None of the UI in Blender is colour managed. That's right. With the exception of the HSV picker, which has a rudimentary bit of management flopped on it by way of the view transform, none of Blender is colour managed. One idiot can only bang on this drum for so long before they get a bit exhausted.

In your particular instance, the colour ramp is mapped from 0.0 to 1.0, which means absolutely nothing under a scene referred model, other than an arbitrary range of values up to 1.0. Filmic uses values that extend up to around 16.0 scene referred, so the colour ramp would need a colour transform selection on it to make it useful in this context.

So it is up to you folks! Filmic was crafted with the hopes of exposing the most basic concepts of colour management to the experienced pixel pusher with the hope that they will take up the torch and put pressure on the software. That is, it is up to you folks to put the pressure on the developers to get the damn software to work properly before adding further fluff.

Another interesting tidbit: Blender won't display correctly on every Apple product since 2015! Curves? Same problems as you cited here. And many, many more including problems of wide gamut references, mangled up blend modes from the display referred Adobe PDF specification, etc!

Good luck!